SOLUTION OF THE DIRICHLET PROBLEM ON A SPHERE FOR THE LAPLACE EQUATION

This work considers the formulation and solution of the Dirichlet problem on a sphere. The domain of the problem is a sphere, and the boundary conditions are given on its surface. The solution is presented in spherical coordinates using the method of separation of variables. A general solution is obtained in the form of a series of spherical functions, and the coefficients of the series are determined from the boundary conditions.